Though this is old, I still would like to clarify based on my experience:
First and foremost there is no such number of how many links to rank top on google. Basically there are two factors:
1) Backlink quality - Which site we put backlink in and how we put it. For example, if we have bunch of backlinks in low DA sites then high chance it can't rank up in top. Spammy backlinks are also face high chance of punishment, rather than ranking up.
2) The difficulty of the keyword - Not all keyword works the same, some have extremely high competitve rate, some are easy to rank up. Generally the more general a keyword is, the harder to rank up (for example, "health", "currency", "banking", etc...), and the more details a keyword is, the easier to rank. But still, it depends on what field the keyword is about and it need thorough keyword research before going for backlinks.